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15 March 2007 Cm-norms on finite sets and Cm extension criteria
Edward Bierstone, Pierre D. Milman
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Duke Math. J. 137(1): 1-18 (15 March 2007). DOI: 10.1215/S0012-7094-07-13711-6

Abstract

C. Fefferman [F1], [F2] has recently given criteria for a function defined on a compact set ERn to extend to a Cm- or Cm,ω-function. His criteria involve uniformity of the Cm- or Cm,ω-norms for extension from finite subsets SE of cardinality at most a large natural number k# depending only on m and n. We prove that one can take k#=2dimP in both cases, where P denotes the space of polynomials of degree at most m in n variables. We also show that the geometric Cm “paratangent bundle” of E (see [BMP2]) can be defined using limits of distributions supported on 2dimP-1 points

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Edward Bierstone. Pierre D. Milman. "Cm-norms on finite sets and Cm extension criteria." Duke Math. J. 137 (1) 1 - 18, 15 March 2007. https://doi.org/10.1215/S0012-7094-07-13711-6

Information

Published: 15 March 2007
First available in Project Euclid: 8 March 2007

zbMATH: 1116.58005
MathSciNet: MR2309142
Digital Object Identifier: 10.1215/S0012-7094-07-13711-6

Subjects:
Primary: 58C25
Secondary: 26B05 , 26B35 , 58A20

Rights: Copyright © 2007 Duke University Press

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Vol.137 • No. 1 • 15 March 2007
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